2 Answers
2

Smeagol was a Stoor Hobbit before the ring corrupted him. This means he was from Gladden Fields just east of the Misty Mountains.

According to the link below he did go searching for the ring but he waited until 2 years after Bilbo took the ring. He spent almost the next 60 years either searching or being captured.

I reckon he never went to the Shire because he didn't know where it was. Shire Hobbits didn't seem knowledgable about things outside of the Shire so I imagine Stoor Hobbits would be the same. I'd say its safe to assume that Smeagol was never west of the Misty Mountains so he'd know nothing of that land. Also I can't see Gollum asking someone for directions to the Shire so he'd have no way of knowing where it is.

The Fellowship of the Ring contains a description from Gandalf about his thoughts about what happens after Bilbo takes the ring.

Gollum is afraid of the light after so many years living under the misty mountains so it takes some time before he leaves them to search for the ring. Gandalf then surmises that, because of his very long association with the ring, he is drawn by Sauron's growing power and makes his way south to Mordor and is eventually captured and tortured.

All Gollum knows is that the ring was taken by 'Bagginses' from 'The Shire', but from his actions clearly doesn't know where that is.

He knows about the Shire as when hes being tortured he says "Baggins...Shire". In the movie that is. Your right about Mordor however, I've reread the first few chapters since I asked the question. He makes his way to Mordor. After this he is imprisoned by the elves. He then escapes from the elves.
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TravisJan 21 '13 at 14:41

@Travis - Sorry - I meant 'doesn't know where he lives' to mean he doesn't know where The Shire is. I will edit.
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iandotkelly♦Jan 21 '13 at 14:56

ah I see..Two good answers but because PriestVallon was first I'll have to accept that one
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TravisJan 21 '13 at 14:58